What Drink Contains The Following Ingredients : 2 Dashes Bitters ; 3/4 Oz Dry Vermouth ; And 3/4 Oz Gin?

A cocktail containing gin and dry vermouth sounds like a variation on the classic martini, but martinis generally don't have bitters as an ingredient, unless you've a very sweet tooth. The recipe you give sounds close to an Attention Cocktail.

Writing in 1951, American cocktail expert Patrick Gavin Duffy gave the recipe for an Attention Cocktail as follows:

1/4 French Vermouth, 1/4 Absinthe, 1/4 Gin, 1/4 Creme de Violette, 2 dashes of Orange Bitters. Stir well with cracked ice and strain.

A modern variation:

1 1/2 oz Gin, 3/4 oz Dry Vermouth, 1/4 oz Violet Liqueur, 2 dashes absinthe, 2 dashes Orange Bitters.

Duffy's recipe for a Sweet Martini:

2/3 Gin, 1/3 Italian Vermouth, 2 dashes Gum Syrup, 1 dash Orange Bitters. Stir well with ice, strain and serve with a cherry.

Here's a few more gin-based cocktails to try: